What is 8.75 as a fraction?

Converting decimals to fractions is an essential skill. It bridges the gap between two numeric representations. In this guide, we will detail the process of converting 8.75 to a fraction.

You can select other values to familiarize yourself with the conversion guide.

Often, convert 8.7 to a fraction or 8.8 to a fraction, depending on the task.

Understanding the decimal: “8.75”

A decimal number has an integer and fractional parts. The decimal point separates the two. The integer is to the left, the fraction to the right. For example, in 8.75, 8 is the integer and 75 is the fraction.

Conversion Explanation:

  1. For the numerator:
    • We start with the number 8.75.
    • By removing the decimal point, we derive the numerator as 875.
  2. For the denominator:
    • Each position after the decimal represents a division by 10.
    • Thus, having 2 positions after the decimal equates to 100 or 102.
  3. Factors:
    • The factors for the numerator and the denominator are numbers that can evenly divide each of them.
    • For instance, the factors of 875 include 1, 5, 7, 25, 35, 125, 175, and 875.
    • The factors of 100 comprise 1, 2, 4, 5, 10, 20, 25, 50, and 100.
  4. Greatest Common Divisor (GCD):
    • It's the largest number that can evenly divide both the numerator and the denominator.
    • In this instance, the GCD for 875 and 100 is 25.

The factors of 875 are:

1 5 7 25 35 125 175 875

The factors of 100 are:

1 2 4 5 10 20 25 50 100

Conversion formula (equation):

8.75=8.751=8.75 × 1001 × 100=875100=875÷25100÷25=354

Solution:

8.75 = 354

What is a decimal?

A decimal is a numeral system with a point. This point divides the integer from its fractional part. It provides a straightforward way to express and work with values less than one.

What is a fraction?

A fraction is a mathematical expression of two parts: the numerator on top and the denominator below. It represents partial values, showcasing relationships or comparisons.

A fast guide to the conversion:

Numbers exist in different formats: decimals, fractions, and percentages. Today, we'll convert the decimal 8.75 into its fractional form. This conversion shows the core essence of the number. And making mathematical operations more intuitive.

Step-by-step solution:

  • Step 1: Laying the groundwork. Before diving into conversion, let's frame our decimal as a fraction over 1. This offers a clean slate, making the subsequent steps systematic. 8.75 = 8.751
  • Step 2: Gauging the decimal's depth. Decimals vary. Some are short; others are long. Our focus? The number of digits after the decimal point. For 8.75, we have three digits. This insight nudges us to elevate our fraction by a factor of 10 for each digit. Factor = 102 = 100
  • Step 3: Amplifying the fraction. Taking our coefficient, it's time to strengthen both the numerator and denominator. The intent? To equalize the fraction by the depth of the decimal. 8.75 × 1001 × 100 = 875100
  • Step 4: Simplifying. Elegance lies in simplicity. Our mission now is to shorten the 875100. This requires seeking common divisors. Here, 25 is our ally, dividing both parts seamlessly. 875 ÷ 25100 ÷ 25 = 354

Conclusion:

The decimal 8.75, when unfurled and explored, translates seamlessly into the fraction 8.75/1. This manual provides an introduction to numbers and deepens number skills. Such conversions, though seemingly elementary, pave the way for advanced mathematical prowess.

Answer in mixed fraction format:

8.75 =
8
3
4